Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-8y &= 9 \\ -8x-9y &= 3\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-9y = 8x+3$ Divide both sides by $-9$ to isolate $y$ $y = {-\dfrac{8}{9}x - \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $-5x-8({-\dfrac{8}{9}x - \dfrac{1}{3}}) = 9$ $-5x + \dfrac{64}{9}x + \dfrac{8}{3} = 9$ Simplify by combining terms, then solve for $x$ $\dfrac{19}{9}x + \dfrac{8}{3} = 9$ $\dfrac{19}{9}x = \dfrac{19}{3}$ $x = 3$ Substitute $3$ for $x$ back into the top equation. $-5( 3)-8y = 9$ $-15-8y = 9$ $-8y = 24$ $y = -3$ The solution is $\enspace x = 3, \enspace y = -3$.